Peel and quarter the potatoes, then shred them finely. Chop off the individual florets of the cauliflower and run them through a food processor, pulsing until they're pea-sized.

In a large bowl, mix the cauliflower and potatoes together. Add the onion, eggs, flour, green onions, salt, pepper, parsley and cheese, and mix thoroughly.

Heat olive oil in a flat-bottomed skillet and preheat the oven to 250º F.

Form 3-inch patties from the cauliflower mixture and place them in hot oil. Cook each patty for 3-5 minutes per side, or until golden-brown and crunchy.

Place each finished patty on a baking sheet, and place baking sheet in the oven to keep patties warm. Snip chives over the top of the patties, and serve them immediately with sour cream.